On Markovian modelling of arrival processes

Markovian arrival process (MAP) is a popular tool for modeling arrival processes of stochastic systems such as queueing systems, reliability systems and telecommunications networks. In this paper we show how properties of Markovian Arrival Processes can be derived from the general theory of Markov processes with a homogeneous second component. We also present a series of results on queueing systems with MAP arrivals which were published in RUDN University before 1990. © 2018, Springer-Verlag GmbH Germany, part of Springer Nature.